{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure4-1(scatter plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T14:37:02.664863Z",
     "start_time": "2019-04-15T14:37:02.266Z"
    }
   },
   "outputs": [],
   "source": [
    "library(ggplot2)\n",
    "# set the path\n",
    "setwd(getwd())\n",
    "# load data\n",
    "lung <- read.csv(\"../psds_data/LungDisease.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T14:37:26.259946Z",
     "start_time": "2019-04-15T14:37:26.227Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t122 obs. of  2 variables:\n",
      " $ PEFR    : int  390 410 430 460 420 280 420 520 610 590 ...\n",
      " $ Exposure: int  0 0 0 0 1 2 2 2 3 3 ...\n"
     ]
    }
   ],
   "source": [
    "str(lung)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:03:48.820913Z",
     "start_time": "2019-04-15T15:03:48.602Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Cu993ILY7rbeNn7XuYWnm9k72nTSyxYkx6sUNcSxdxWCVbJD1jZmwKHrVPnpiJg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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=5, repr.plot.height=4)  # plot size\n",
    "p <- ggplot(lung, aes(x=Exposure, y=PEFR)) + geom_point(shape=1)\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure4-3(Regression plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T14:42:49.693196Z",
     "start_time": "2019-04-15T14:42:49.657Z"
    }
   },
   "outputs": [],
   "source": [
    "model <- lm(PEFR ~ Exposure, data=lung)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:04:00.252098Z",
     "start_time": "2019-04-15T15:04:00.027Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Bzjz4xKRT4WV5sYrAfe9X+cW6uy0EGXCDfk7N2b2nmvVfWHnz8tKWv2Qp6Ddd65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\nAAukiP4Pp/I3OWVWlFAAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b0 <- model$coefficients[1]\n",
    "b1 <- model$coefficients[2]\n",
    "p + geom_abline(slope = b1, intercept = b0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:14:57.572665Z",
     "start_time": "2019-04-15T15:14:57.296Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>AdjSalePrice</th><th scope=col>SqFtTotLiving</th><th scope=col>SqFtLot</th><th scope=col>Bathrooms</th><th scope=col>Bedrooms</th><th scope=col>BldgGrade</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 300805</td><td>2400   </td><td> 9373  </td><td>3.00   </td><td>6      </td><td> 7     </td></tr>\n",
       "\t<tr><td>1076162</td><td>3764   </td><td>20156  </td><td>3.75   </td><td>4      </td><td>10     </td></tr>\n",
       "\t<tr><td> 761805</td><td>2060   </td><td>26036  </td><td>1.75   </td><td>4      </td><td> 8     </td></tr>\n",
       "\t<tr><td> 442065</td><td>3200   </td><td> 8618  </td><td>3.75   </td><td>5      </td><td> 7     </td></tr>\n",
       "\t<tr><td> 297065</td><td>1720   </td><td> 8620  </td><td>1.75   </td><td>4      </td><td> 7     </td></tr>\n",
       "\t<tr><td> 411781</td><td> 930   </td><td> 1012  </td><td>1.50   </td><td>2      </td><td> 8     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       " AdjSalePrice & SqFtTotLiving & SqFtLot & Bathrooms & Bedrooms & BldgGrade\\\\\n",
       "\\hline\n",
       "\t  300805 & 2400    &  9373   & 3.00    & 6       &  7     \\\\\n",
       "\t 1076162 & 3764    & 20156   & 3.75    & 4       & 10     \\\\\n",
       "\t  761805 & 2060    & 26036   & 1.75    & 4       &  8     \\\\\n",
       "\t  442065 & 3200    &  8618   & 3.75    & 5       &  7     \\\\\n",
       "\t  297065 & 1720    &  8620   & 1.75    & 4       &  7     \\\\\n",
       "\t  411781 &  930    &  1012   & 1.50    & 2       &  8     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| AdjSalePrice | SqFtTotLiving | SqFtLot | Bathrooms | Bedrooms | BldgGrade |\n",
       "|---|---|---|---|---|---|\n",
       "|  300805 | 2400    |  9373   | 3.00    | 6       |  7      |\n",
       "| 1076162 | 3764    | 20156   | 3.75    | 4       | 10      |\n",
       "|  761805 | 2060    | 26036   | 1.75    | 4       |  8      |\n",
       "|  442065 | 3200    |  8618   | 3.75    | 5       |  7      |\n",
       "|  297065 | 1720    |  8620   | 1.75    | 4       |  7      |\n",
       "|  411781 |  930    |  1012   | 1.50    | 2       |  8      |\n",
       "\n"
      ],
      "text/plain": [
       "  AdjSalePrice SqFtTotLiving SqFtLot Bathrooms Bedrooms BldgGrade\n",
       "1  300805      2400           9373   3.00      6         7       \n",
       "2 1076162      3764          20156   3.75      4        10       \n",
       "3  761805      2060          26036   1.75      4         8       \n",
       "4  442065      3200           8618   3.75      5         7       \n",
       "5  297065      1720           8620   1.75      4         7       \n",
       "6  411781       930           1012   1.50      2         8       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "house <- read.csv(\"../psds_data/house_sales.csv\", sep = '\\t')\n",
    "head(house[, c(\"AdjSalePrice\", \"SqFtTotLiving\", \"SqFtLot\", \"Bathrooms\", \n",
    "               \"Bedrooms\", \"BldgGrade\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:15:48.266003Z",
     "start_time": "2019-04-15T15:15:48.209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
       "    Bedrooms + BldgGrade, data = house, na.action = na.omit)\n",
       "\n",
       "Coefficients:\n",
       "  (Intercept)  SqFtTotLiving        SqFtLot      Bathrooms       Bedrooms  \n",
       "   -5.219e+05      2.288e+02     -6.051e-02     -1.944e+04     -4.778e+04  \n",
       "    BldgGrade  \n",
       "    1.061e+05  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "house_lm <- lm(AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
    "                 Bedrooms + BldgGrade,  \n",
    "               data=house, na.action=na.omit)\n",
    "house_lm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:15:59.853799Z",
     "start_time": "2019-04-15T15:15:59.740Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
       "    Bedrooms + BldgGrade, data = house, na.action = na.omit)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1199508  -118879   -20982    87414  9472982 \n",
       "\n",
       "Coefficients:\n",
       "                Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   -5.219e+05  1.565e+04 -33.349  < 2e-16 ***\n",
       "SqFtTotLiving  2.288e+02  3.898e+00  58.699  < 2e-16 ***\n",
       "SqFtLot       -6.051e-02  6.118e-02  -0.989    0.323    \n",
       "Bathrooms     -1.944e+04  3.625e+03  -5.362 8.32e-08 ***\n",
       "Bedrooms      -4.778e+04  2.489e+03 -19.194  < 2e-16 ***\n",
       "BldgGrade      1.061e+05  2.396e+03  44.287  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 261200 on 22683 degrees of freedom\n",
       "Multiple R-squared:  0.5407,\tAdjusted R-squared:  0.5406 \n",
       "F-statistic:  5340 on 5 and 22683 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(house_lm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Selection and Stepwise Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:18:05.496589Z",
     "start_time": "2019-04-15T15:18:05.435Z"
    }
   },
   "outputs": [],
   "source": [
    "house_full <- lm(AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
    "                   Bedrooms + BldgGrade + PropertyType + NbrLivingUnits + \n",
    "                   SqFtFinBasement + YrBuilt + YrRenovated + NewConstruction,\n",
    "                 data=house, na.action=na.omit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:18:33.136516Z",
     "start_time": "2019-04-15T15:18:31.742Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start:  AIC=563193.9\n",
      "AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms + \n",
      "    BldgGrade + PropertyType + NbrLivingUnits + SqFtFinBasement + \n",
      "    YrBuilt + YrRenovated + NewConstruction\n",
      "\n",
      "                  Df  Sum of Sq        RSS    AIC\n",
      "- NbrLivingUnits   1 6.4936e+09 1.3662e+15 563192\n",
      "- NewConstruction  1 1.0188e+10 1.3662e+15 563192\n",
      "- YrRenovated      1 2.4839e+10 1.3662e+15 563192\n",
      "- SqFtLot          1 1.0643e+11 1.3663e+15 563194\n",
      "<none>                          1.3662e+15 563194\n",
      "- SqFtFinBasement  1 1.3984e+11 1.3664e+15 563194\n",
      "- PropertyType     2 4.4129e+12 1.3706e+15 563263\n",
      "- Bathrooms        1 7.6340e+12 1.3739e+15 563318\n",
      "- Bedrooms         1 2.8246e+13 1.3945e+15 563656\n",
      "- YrBuilt          1 1.2905e+14 1.4953e+15 565240\n",
      "- SqFtTotLiving    1 1.3265e+14 1.4989e+15 565294\n",
      "- BldgGrade        1 1.9059e+14 1.5568e+15 566155\n",
      "\n",
      "Step:  AIC=563192.1\n",
      "AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms + \n",
      "    BldgGrade + PropertyType + SqFtFinBasement + YrBuilt + YrRenovated + \n",
      "    NewConstruction\n",
      "\n",
      "                  Df  Sum of Sq        RSS    AIC\n",
      "- NewConstruction  1 1.0394e+10 1.3662e+15 563190\n",
      "- YrRenovated      1 2.5399e+10 1.3663e+15 563190\n",
      "- SqFtLot          1 1.0717e+11 1.3663e+15 563192\n",
      "<none>                          1.3662e+15 563192\n",
      "- SqFtFinBasement  1 1.3781e+11 1.3664e+15 563192\n",
      "+ NbrLivingUnits   1 6.4936e+09 1.3662e+15 563194\n",
      "- PropertyType     2 4.4221e+12 1.3706e+15 563261\n",
      "- Bathrooms        1 7.7519e+12 1.3740e+15 563318\n",
      "- Bedrooms         1 2.8308e+13 1.3945e+15 563655\n",
      "- YrBuilt          1 1.3011e+14 1.4963e+15 565254\n",
      "- SqFtTotLiving    1 1.3288e+14 1.4991e+15 565296\n",
      "- BldgGrade        1 1.9186e+14 1.5581e+15 566172\n",
      "\n",
      "Step:  AIC=563190.2\n",
      "AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms + \n",
      "    BldgGrade + PropertyType + SqFtFinBasement + YrBuilt + YrRenovated\n",
      "\n",
      "                  Df  Sum of Sq        RSS    AIC\n",
      "- YrRenovated      1 2.5655e+10 1.3663e+15 563189\n",
      "- SqFtLot          1 1.1468e+11 1.3664e+15 563190\n",
      "<none>                          1.3662e+15 563190\n",
      "- SqFtFinBasement  1 1.4477e+11 1.3664e+15 563191\n",
      "+ NewConstruction  1 1.0394e+10 1.3662e+15 563192\n",
      "+ NbrLivingUnits   1 6.7000e+09 1.3662e+15 563192\n",
      "- PropertyType     2 4.5236e+12 1.3708e+15 563261\n",
      "- Bathrooms        1 7.7505e+12 1.3740e+15 563317\n",
      "- Bedrooms         1 2.8304e+13 1.3945e+15 563653\n",
      "- SqFtTotLiving    1 1.3391e+14 1.5001e+15 565310\n",
      "- YrBuilt          1 1.3757e+14 1.5038e+15 565365\n",
      "- BldgGrade        1 1.9253e+14 1.5588e+15 566179\n",
      "\n",
      "Step:  AIC=563188.7\n",
      "AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms + \n",
      "    BldgGrade + PropertyType + SqFtFinBasement + YrBuilt\n",
      "\n",
      "                  Df  Sum of Sq        RSS    AIC\n",
      "- SqFtLot          1 1.1399e+11 1.3664e+15 563189\n",
      "<none>                          1.3663e+15 563189\n",
      "- SqFtFinBasement  1 1.4938e+11 1.3664e+15 563189\n",
      "+ YrRenovated      1 2.5655e+10 1.3662e+15 563190\n",
      "+ NewConstruction  1 1.0651e+10 1.3663e+15 563190\n",
      "+ NbrLivingUnits   1 7.2737e+09 1.3663e+15 563191\n",
      "- PropertyType     2 4.5012e+12 1.3708e+15 563259\n",
      "- Bathrooms        1 7.7815e+12 1.3740e+15 563316\n",
      "- Bedrooms         1 2.8286e+13 1.3945e+15 563652\n",
      "- SqFtTotLiving    1 1.3389e+14 1.5002e+15 565308\n",
      "- YrBuilt          1 1.5088e+14 1.5171e+15 565563\n",
      "- BldgGrade        1 1.9253e+14 1.5588e+15 566178\n",
      "\n",
      "Step:  AIC=563188.5\n",
      "AdjSalePrice ~ SqFtTotLiving + Bathrooms + Bedrooms + BldgGrade + \n",
      "    PropertyType + SqFtFinBasement + YrBuilt\n",
      "\n",
      "                  Df  Sum of Sq        RSS    AIC\n",
      "<none>                          1.3664e+15 563189\n",
      "+ SqFtLot          1 1.1399e+11 1.3663e+15 563189\n",
      "- SqFtFinBasement  1 1.4058e+11 1.3665e+15 563189\n",
      "+ YrRenovated      1 2.4965e+10 1.3664e+15 563190\n",
      "+ NewConstruction  1 1.8206e+10 1.3664e+15 563190\n",
      "+ NbrLivingUnits   1 8.1478e+09 1.3664e+15 563190\n",
      "- PropertyType     2 4.4353e+12 1.3708e+15 563258\n",
      "- Bathrooms        1 7.7135e+12 1.3741e+15 563314\n",
      "- Bedrooms         1 2.8588e+13 1.3950e+15 563656\n",
      "- SqFtTotLiving    1 1.3750e+14 1.5039e+15 565362\n",
      "- YrBuilt          1 1.5077e+14 1.5171e+15 565561\n",
      "- BldgGrade        1 1.9243e+14 1.5588e+15 566176\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ SqFtTotLiving + Bathrooms + Bedrooms + \n",
       "    BldgGrade + PropertyType + SqFtFinBasement + YrBuilt, data = house, \n",
       "    na.action = na.omit)\n",
       "\n",
       "Coefficients:\n",
       "              (Intercept)              SqFtTotLiving  \n",
       "                6.178e+06                  1.993e+02  \n",
       "                Bathrooms                   Bedrooms  \n",
       "                4.240e+04                 -5.197e+04  \n",
       "                BldgGrade  PropertyTypeSingle Family  \n",
       "                1.372e+05                  2.285e+04  \n",
       "    PropertyTypeTownhouse            SqFtFinBasement  \n",
       "                8.438e+04                  7.032e+00  \n",
       "                  YrBuilt  \n",
       "               -3.565e+03  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS)\n",
    "step <- stepAIC(house_full, direction=\"both\")\n",
    "step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weighted Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:20:30.647166Z",
     "start_time": "2019-04-15T15:20:30.539Z"
    }
   },
   "outputs": [],
   "source": [
    "library(lubridate)\n",
    "house$Year <- year(house$DocumentDate)\n",
    "house$Weight <- house$Year - 2005"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:23:34.509238Z",
     "start_time": "2019-04-15T15:23:34.417Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>house_lm</th><th scope=col>house_wt</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>-521924.722</td><td>-584265.244</td></tr>\n",
       "\t<tr><th scope=row>SqFtTotLiving</th><td>    228.832</td><td>    245.017</td></tr>\n",
       "\t<tr><th scope=row>SqFtLot</th><td>     -0.061</td><td>     -0.292</td></tr>\n",
       "\t<tr><th scope=row>Bathrooms</th><td> -19438.099</td><td> -26079.171</td></tr>\n",
       "\t<tr><th scope=row>Bedrooms</th><td> -47781.153</td><td> -53625.404</td></tr>\n",
       "\t<tr><th scope=row>BldgGrade</th><td> 106117.210</td><td> 115259.026</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & house\\_lm & house\\_wt\\\\\n",
       "\\hline\n",
       "\t(Intercept) & -521924.722 & -584265.244\\\\\n",
       "\tSqFtTotLiving &     228.832 &     245.017\\\\\n",
       "\tSqFtLot &      -0.061 &      -0.292\\\\\n",
       "\tBathrooms &  -19438.099 &  -26079.171\\\\\n",
       "\tBedrooms &  -47781.153 &  -53625.404\\\\\n",
       "\tBldgGrade &  106117.210 &  115259.026\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | house_lm | house_wt |\n",
       "|---|---|---|\n",
       "| (Intercept) | -521924.722 | -584265.244 |\n",
       "| SqFtTotLiving |     228.832 |     245.017 |\n",
       "| SqFtLot |      -0.061 |      -0.292 |\n",
       "| Bathrooms |  -19438.099 |  -26079.171 |\n",
       "| Bedrooms |  -47781.153 |  -53625.404 |\n",
       "| BldgGrade |  106117.210 |  115259.026 |\n",
       "\n"
      ],
      "text/plain": [
       "              house_lm    house_wt   \n",
       "(Intercept)   -521924.722 -584265.244\n",
       "SqFtTotLiving     228.832     245.017\n",
       "SqFtLot            -0.061      -0.292\n",
       "Bathrooms      -19438.099  -26079.171\n",
       "Bedrooms       -47781.153  -53625.404\n",
       "BldgGrade      106117.210  115259.026"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "house_wt <- lm(AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms + BldgGrade,\n",
    "              data = house, weights=Weight)\n",
    "round(cbind(house_lm=house_lm$coefficients, house_wt=house_wt$coefficients), 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factor Variables in Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dummy Variables Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:25:37.642695Z",
     "start_time": "2019-04-15T15:25:37.611Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>Multiplex</li>\n",
       "\t<li>Single Family</li>\n",
       "\t<li>Single Family</li>\n",
       "\t<li>Single Family</li>\n",
       "\t<li>Single Family</li>\n",
       "\t<li>Townhouse</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'Multiplex'</li>\n",
       "\t\t<li>'Single Family'</li>\n",
       "\t\t<li>'Townhouse'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item Multiplex\n",
       "\\item Single Family\n",
       "\\item Single Family\n",
       "\\item Single Family\n",
       "\\item Single Family\n",
       "\\item Townhouse\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'Multiplex'\n",
       "\\item 'Single Family'\n",
       "\\item 'Townhouse'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. Multiplex\n",
       "2. Single Family\n",
       "3. Single Family\n",
       "4. Single Family\n",
       "5. Single Family\n",
       "6. Townhouse\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. 'Multiplex'\n",
       "2. 'Single Family'\n",
       "3. 'Townhouse'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] Multiplex     Single Family Single Family Single Family Single Family\n",
       "[6] Townhouse    \n",
       "Levels: Multiplex Single Family Townhouse"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(house[, \"PropertyType\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:26:29.167717Z",
     "start_time": "2019-04-15T15:26:29.129Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>PropertyTypeMultiplex</th><th scope=col>PropertyTypeSingle Family</th><th scope=col>PropertyTypeTownhouse</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " PropertyTypeMultiplex & PropertyTypeSingle Family & PropertyTypeTownhouse\\\\\n",
       "\\hline\n",
       "\t 1 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0\\\\\n",
       "\t 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| PropertyTypeMultiplex | PropertyTypeSingle Family | PropertyTypeTownhouse |\n",
       "|---|---|---|\n",
       "| 1 | 0 | 0 |\n",
       "| 0 | 1 | 0 |\n",
       "| 0 | 1 | 0 |\n",
       "| 0 | 1 | 0 |\n",
       "| 0 | 1 | 0 |\n",
       "| 0 | 0 | 1 |\n",
       "\n"
      ],
      "text/plain": [
       "  PropertyTypeMultiplex PropertyTypeSingle Family PropertyTypeTownhouse\n",
       "1 1                     0                         0                    \n",
       "2 0                     1                         0                    \n",
       "3 0                     1                         0                    \n",
       "4 0                     1                         0                    \n",
       "5 0                     1                         0                    \n",
       "6 0                     0                         1                    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用one hot encoding（去除截距项）\n",
    "prop_type_dummies <- model.matrix(~PropertyType - 1, data=house)\n",
    "head(prop_type_dummies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:40:45.140619Z",
     "start_time": "2019-04-15T15:40:45.090Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
       "    Bedrooms + BldgGrade + PropertyType, data = house)\n",
       "\n",
       "Coefficients:\n",
       "              (Intercept)              SqFtTotLiving  \n",
       "               -4.469e+05                  2.234e+02  \n",
       "                  SqFtLot                  Bathrooms  \n",
       "               -7.041e-02                 -1.597e+04  \n",
       "                 Bedrooms                  BldgGrade  \n",
       "               -5.090e+04                  1.094e+05  \n",
       "PropertyTypeSingle Family      PropertyTypeTownhouse  \n",
       "               -8.469e+04                 -1.151e+05  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 默认采取另外的编码方式(保留截距项)\n",
    "lm(AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + Bedrooms \n",
    "   + BldgGrade + PropertyType, data = house)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Factor Variables with Many Levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:42:52.367975Z",
     "start_time": "2019-04-15T15:42:52.328Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       " 9800 89118 98001 98002 98003 98004 98005 98006 98007 98008 98010 98011 98014 \n",
       "    1     1   358   180   241   293   133   460   112   291    56   163    85 \n",
       "98019 98022 98023 98024 98027 98028 98029 98030 98031 98032 98033 98034 98038 \n",
       "  242   188   455    31   366   252   475   263   308   121   517   575   788 \n",
       "98039 98040 98042 98043 98045 98047 98050 98051 98052 98053 98055 98056 98057 \n",
       "   47   244   641     1   222    48     7    32   614   499   332   402     4 \n",
       "98058 98059 98065 98068 98070 98072 98074 98075 98077 98092 98102 98103 98105 \n",
       "  420   513   430     1    89   245   502   388   204   289   106   671   313 \n",
       "98106 98107 98108 98109 98112 98113 98115 98116 98117 98118 98119 98122 98125 \n",
       "  361   296   155   149   357     1   620   364   619   492   260   380   409 \n",
       "98126 98133 98136 98144 98146 98148 98155 98166 98168 98177 98178 98188 98198 \n",
       "  473   465   310   332   287    40   358   193   332   216   266   101   225 \n",
       "98199 98224 98288 98354 \n",
       "  393     3     4     9 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(house$ZipCode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:44:18.786240Z",
     "start_time": "2019-04-15T15:44:18.649Z"
    }
   },
   "outputs": [],
   "source": [
    "library(dplyr)\n",
    "zip_groups <- house %>%\n",
    "  mutate(resid = residuals(house_lm)) %>%\n",
    "  group_by(ZipCode) %>%\n",
    "  summarize(med_resid = median(resid),\n",
    "            cnt = n()) %>%\n",
    "  # sort the zip codes by the median residual\n",
    "  arrange(med_resid) %>%\n",
    "  mutate(cum_cnt = cumsum(cnt),\n",
    "         ZipGroup = factor(ntile(cum_cnt, 5)))\n",
    "house <- house %>%\n",
    "  left_join(select(zip_groups, ZipCode, ZipGroup), by='ZipCode')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:53:36.819945Z",
     "start_time": "2019-04-15T15:53:36.772Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>DocumentDate</th><th scope=col>SalePrice</th><th scope=col>PropertyID</th><th scope=col>PropertyType</th><th scope=col>ym</th><th scope=col>zhvi_px</th><th scope=col>zhvi_idx</th><th scope=col>AdjSalePrice</th><th scope=col>NbrLivingUnits</th><th scope=col>SqFtLot</th><th scope=col>⋯</th><th scope=col>YrBuilt</th><th scope=col>YrRenovated</th><th scope=col>TrafficNoise</th><th scope=col>LandVal</th><th scope=col>ImpsVal</th><th scope=col>ZipCode</th><th scope=col>NewConstruction</th><th scope=col>Year</th><th scope=col>Weight</th><th scope=col>ZipGroup</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>2014-09-16   </td><td> 280000      </td><td>1000102      </td><td>Multiplex    </td><td>2014-09-01   </td><td>405100       </td><td>0.9308364    </td><td> 300805      </td><td>2            </td><td> 9373        </td><td>⋯            </td><td>1991         </td><td>0            </td><td>0            </td><td> 70000       </td><td>229000       </td><td>98002        </td><td>FALSE        </td><td>2014         </td><td>9            </td><td>3            </td></tr>\n",
       "\t<tr><td>2006-06-16   </td><td>1000000      </td><td>1200013      </td><td>Single Family</td><td>2006-06-01   </td><td>404400       </td><td>0.9292279    </td><td>1076162      </td><td>1            </td><td>20156        </td><td>⋯            </td><td>2005         </td><td>0            </td><td>0            </td><td>203000       </td><td>590000       </td><td>98166        </td><td> TRUE        </td><td>2006         </td><td>1            </td><td>3            </td></tr>\n",
       "\t<tr><td>2007-01-29   </td><td> 745000      </td><td>1200019      </td><td>Single Family</td><td>2007-01-01   </td><td>425600       </td><td>0.9779412    </td><td> 761805      </td><td>1            </td><td>26036        </td><td>⋯            </td><td>1947         </td><td>0            </td><td>0            </td><td>183000       </td><td>275000       </td><td>98166        </td><td>FALSE        </td><td>2007         </td><td>2            </td><td>3            </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllllllllllllllll}\n",
       " DocumentDate & SalePrice & PropertyID & PropertyType & ym & zhvi\\_px & zhvi\\_idx & AdjSalePrice & NbrLivingUnits & SqFtLot & ⋯ & YrBuilt & YrRenovated & TrafficNoise & LandVal & ImpsVal & ZipCode & NewConstruction & Year & Weight & ZipGroup\\\\\n",
       "\\hline\n",
       "\t 2014-09-16    &  280000       & 1000102       & Multiplex     & 2014-09-01    & 405100        & 0.9308364     &  300805       & 2             &  9373         & ⋯             & 1991          & 0             & 0             &  70000        & 229000        & 98002         & FALSE         & 2014          & 9             & 3            \\\\\n",
       "\t 2006-06-16    & 1000000       & 1200013       & Single Family & 2006-06-01    & 404400        & 0.9292279     & 1076162       & 1             & 20156         & ⋯             & 2005          & 0             & 0             & 203000        & 590000        & 98166         &  TRUE         & 2006          & 1             & 3            \\\\\n",
       "\t 2007-01-29    &  745000       & 1200019       & Single Family & 2007-01-01    & 425600        & 0.9779412     &  761805       & 1             & 26036         & ⋯             & 1947          & 0             & 0             & 183000        & 275000        & 98166         & FALSE         & 2007          & 2             & 3            \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| DocumentDate | SalePrice | PropertyID | PropertyType | ym | zhvi_px | zhvi_idx | AdjSalePrice | NbrLivingUnits | SqFtLot | ⋯ | YrBuilt | YrRenovated | TrafficNoise | LandVal | ImpsVal | ZipCode | NewConstruction | Year | Weight | ZipGroup |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2014-09-16    |  280000       | 1000102       | Multiplex     | 2014-09-01    | 405100        | 0.9308364     |  300805       | 2             |  9373         | ⋯             | 1991          | 0             | 0             |  70000        | 229000        | 98002         | FALSE         | 2014          | 9             | 3             |\n",
       "| 2006-06-16    | 1000000       | 1200013       | Single Family | 2006-06-01    | 404400        | 0.9292279     | 1076162       | 1             | 20156         | ⋯             | 2005          | 0             | 0             | 203000        | 590000        | 98166         |  TRUE         | 2006          | 1             | 3             |\n",
       "| 2007-01-29    |  745000       | 1200019       | Single Family | 2007-01-01    | 425600        | 0.9779412     |  761805       | 1             | 26036         | ⋯             | 1947          | 0             | 0             | 183000        | 275000        | 98166         | FALSE         | 2007          | 2             | 3             |\n",
       "\n"
      ],
      "text/plain": [
       "  DocumentDate SalePrice PropertyID PropertyType  ym         zhvi_px zhvi_idx \n",
       "1 2014-09-16    280000   1000102    Multiplex     2014-09-01 405100  0.9308364\n",
       "2 2006-06-16   1000000   1200013    Single Family 2006-06-01 404400  0.9292279\n",
       "3 2007-01-29    745000   1200019    Single Family 2007-01-01 425600  0.9779412\n",
       "  AdjSalePrice NbrLivingUnits SqFtLot ⋯ YrBuilt YrRenovated TrafficNoise\n",
       "1  300805      2               9373   ⋯ 1991    0           0           \n",
       "2 1076162      1              20156   ⋯ 2005    0           0           \n",
       "3  761805      1              26036   ⋯ 1947    0           0           \n",
       "  LandVal ImpsVal ZipCode NewConstruction Year Weight ZipGroup\n",
       "1  70000  229000  98002   FALSE           2014 9      3       \n",
       "2 203000  590000  98166    TRUE           2006 1      3       \n",
       "3 183000  275000  98166   FALSE           2007 2      3       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(house, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting the Regression Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlated Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:58:46.304646Z",
     "start_time": "2019-04-15T15:58:46.273Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>6177658.14374458</dd>\n",
       "\t<dt>SqFtTotLiving</dt>\n",
       "\t\t<dd>199.274742175447</dd>\n",
       "\t<dt>Bathrooms</dt>\n",
       "\t\t<dd>42403.0599996766</dd>\n",
       "\t<dt>Bedrooms</dt>\n",
       "\t\t<dd>-51974.7684556787</dd>\n",
       "\t<dt>BldgGrade</dt>\n",
       "\t\t<dd>137181.137246268</dd>\n",
       "\t<dt>PropertyTypeSingle Family</dt>\n",
       "\t\t<dd>22854.8795401787</dd>\n",
       "\t<dt>PropertyTypeTownhouse</dt>\n",
       "\t\t<dd>84378.9333363938</dd>\n",
       "\t<dt>SqFtFinBasement</dt>\n",
       "\t\t<dd>7.03217891753911</dd>\n",
       "\t<dt>YrBuilt</dt>\n",
       "\t\t<dd>-3564.93487041506</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 6177658.14374458\n",
       "\\item[SqFtTotLiving] 199.274742175447\n",
       "\\item[Bathrooms] 42403.0599996766\n",
       "\\item[Bedrooms] -51974.7684556787\n",
       "\\item[BldgGrade] 137181.137246268\n",
       "\\item[PropertyTypeSingle Family] 22854.8795401787\n",
       "\\item[PropertyTypeTownhouse] 84378.9333363938\n",
       "\\item[SqFtFinBasement] 7.03217891753911\n",
       "\\item[YrBuilt] -3564.93487041506\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   6177658.14374458SqFtTotLiving\n",
       ":   199.274742175447Bathrooms\n",
       ":   42403.0599996766Bedrooms\n",
       ":   -51974.7684556787BldgGrade\n",
       ":   137181.137246268PropertyTypeSingle Family\n",
       ":   22854.8795401787PropertyTypeTownhouse\n",
       ":   84378.9333363938SqFtFinBasement\n",
       ":   7.03217891753911YrBuilt\n",
       ":   -3564.93487041506\n",
       "\n"
      ],
      "text/plain": [
       "              (Intercept)             SqFtTotLiving                 Bathrooms \n",
       "             6.177658e+06              1.992747e+02              4.240306e+04 \n",
       "                 Bedrooms                 BldgGrade PropertyTypeSingle Family \n",
       "            -5.197477e+04              1.371811e+05              2.285488e+04 \n",
       "    PropertyTypeTownhouse           SqFtFinBasement                   YrBuilt \n",
       "             8.437893e+04              7.032179e+00             -3.564935e+03 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 这里书上前面用的`step`,这里又换成`step_lm`...\n",
    "step_lm <- step\n",
    "step_lm$coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T15:59:22.632012Z",
     "start_time": "2019-04-15T15:59:22.588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ Bedrooms + BldgGrade + PropertyType + \n",
       "    YrBuilt, data = house, na.action = na.omit)\n",
       "\n",
       "Coefficients:\n",
       "              (Intercept)                   Bedrooms  \n",
       "                  4913025                      27136  \n",
       "                BldgGrade  PropertyTypeSingle Family  \n",
       "                   249019                     -19932  \n",
       "    PropertyTypeTownhouse                    YrBuilt  \n",
       "                   -47424                      -3211  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "update(step_lm, . ~ . - SqFtTotLiving - SqFtFinBasement - Bathrooms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactions and Main Effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:01:05.211004Z",
     "start_time": "2019-04-15T16:01:05.155Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ SqFtTotLiving * ZipGroup + SqFtLot + \n",
       "    Bathrooms + Bedrooms + BldgGrade + PropertyType, data = house, \n",
       "    na.action = na.omit)\n",
       "\n",
       "Coefficients:\n",
       "              (Intercept)              SqFtTotLiving  \n",
       "               -4.919e+05                  1.176e+02  \n",
       "                ZipGroup2                  ZipGroup3  \n",
       "               -1.342e+04                  2.254e+04  \n",
       "                ZipGroup4                  ZipGroup5  \n",
       "                1.776e+04                 -1.555e+05  \n",
       "                  SqFtLot                  Bathrooms  \n",
       "                7.176e-01                 -5.130e+03  \n",
       "                 Bedrooms                  BldgGrade  \n",
       "               -4.181e+04                  1.053e+05  \n",
       "PropertyTypeSingle Family      PropertyTypeTownhouse  \n",
       "                1.603e+04                 -5.629e+04  \n",
       "  SqFtTotLiving:ZipGroup2    SqFtTotLiving:ZipGroup3  \n",
       "                3.165e+01                  3.893e+01  \n",
       "  SqFtTotLiving:ZipGroup4    SqFtTotLiving:ZipGroup5  \n",
       "                7.051e+01                  2.298e+02  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm(AdjSalePrice ~  SqFtTotLiving*ZipGroup + SqFtLot + \n",
    "     Bathrooms + Bedrooms + \n",
    "     BldgGrade + PropertyType,\n",
    "   data=house, na.action=na.omit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the Assumptions: Regression Diagnostics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:04:02.685314Z",
     "start_time": "2019-04-15T16:04:02.651Z"
    }
   },
   "outputs": [],
   "source": [
    "house_98105 <- house[house$ZipCode == 98105, ]\n",
    "lm_98105 <- lm(AdjSalePrice ~ SqFtTotLiving + SqFtLot + Bathrooms + \n",
    "                 Bedrooms + BldgGrade, data=house_98105)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:04:34.643676Z",
     "start_time": "2019-04-15T16:04:34.605Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>20431:</strong> -4.32673180407856"
      ],
      "text/latex": [
       "\\textbf{20431:} -4.32673180407856"
      ],
      "text/markdown": [
       "**20431:** -4.32673180407856"
      ],
      "text/plain": [
       "    20431 \n",
       "-4.326732 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sredis <- rstandard(lm_98105)\n",
    "idx <- order(sredis)\n",
    "sredis[idx[1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:04:48.948017Z",
     "start_time": "2019-04-15T16:04:48.916Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>AdjSalePrice</th><th scope=col>SqFtTotLiving</th><th scope=col>SqFtLot</th><th scope=col>Bathrooms</th><th scope=col>Bedrooms</th><th scope=col>BldgGrade</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>20431</th><td>119748</td><td>2900  </td><td>7276  </td><td>3     </td><td>6     </td><td>7     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & AdjSalePrice & SqFtTotLiving & SqFtLot & Bathrooms & Bedrooms & BldgGrade\\\\\n",
       "\\hline\n",
       "\t20431 & 119748 & 2900   & 7276   & 3      & 6      & 7     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | AdjSalePrice | SqFtTotLiving | SqFtLot | Bathrooms | Bedrooms | BldgGrade |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 20431 | 119748 | 2900   | 7276   | 3      | 6      | 7      |\n",
       "\n"
      ],
      "text/plain": [
       "      AdjSalePrice SqFtTotLiving SqFtLot Bathrooms Bedrooms BldgGrade\n",
       "20431 119748       2900          7276    3         6        7        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "house_98105[idx[1], c('AdjSalePrice', 'SqFtTotLiving', 'SqFtLot',\n",
    "                      'Bathrooms', 'Bedrooms', 'BldgGrade')]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Influential Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:05:28.072807Z",
     "start_time": "2019-04-15T16:05:27.979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CLL7hCSAlKAOXTPvnvrPCQwvNgepuPJNVkZIwuOI/bBnmJltAPwrZjaKrWiP0BX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\nwgv/B57Y7ewOCA+BAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "std_resid <- rstandard(lm_98105)\n",
    "cooks_D <- cooks.distance(lm_98105)\n",
    "hat_values <- hatvalues(lm_98105)\n",
    "plot(hat_values, std_resid, cex=10*sqrt(cooks_D))\n",
    "abline(h=c(-2.5, 2.5), lty=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Heteroskedasticity, Non-Normality and Correlated Errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:07:54.482242Z",
     "start_time": "2019-04-15T16:07:54.090Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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X19fVJSUmBgYL9+/eLi4o4cOWLe/fciEIG2z9A9QldX16+++mrdunV79uzZtm1b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\nYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df <- data.frame(\n",
    "  resid = residuals(lm_98105),\n",
    "  pred = predict(lm_98105))\n",
    "ggplot(df, aes(pred, abs(resid))) +\n",
    "  geom_point() +\n",
    "  geom_smooth() \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Residual Plots and Nonlinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:10:23.776520Z",
     "start_time": "2019-04-15T16:10:23.747Z"
    }
   },
   "outputs": [],
   "source": [
    "terms <- predict(lm_98105, type='terms')\n",
    "partial_resid <- resid(lm_98105) + terms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:10:36.985300Z",
     "start_time": "2019-04-15T16:10:36.577Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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GuEivASxSbdVoRrhDU1NbJ4iWJdSb4J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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df <- data.frame(SqFtTotLiving = house_98105[, 'SqFtTotLiving'],\n",
    "                 Terms = terms[, 'SqFtTotLiving'],\n",
    "                 PartialResid = partial_resid[, 'SqFtTotLiving'])\n",
    "ggplot(df, aes(SqFtTotLiving, PartialResid)) +\n",
    "  geom_point(shape=1) + scale_shape(solid = FALSE) +\n",
    "  geom_smooth(linetype=2) + \n",
    "  geom_line(aes(SqFtTotLiving, Terms))  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial and Spline Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:11:34.533939Z",
     "start_time": "2019-04-15T16:11:34.499Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ poly(SqFtTotLiving, 2) + SqFtLot + \n",
       "    BldgGrade + Bathrooms + Bedrooms, data = house_98105)\n",
       "\n",
       "Coefficients:\n",
       "            (Intercept)  poly(SqFtTotLiving, 2)1  poly(SqFtTotLiving, 2)2  \n",
       "             -402530.47               3271519.49                776934.02  \n",
       "                SqFtLot                BldgGrade                Bathrooms  \n",
       "                  32.56                135717.06                 -1435.12  \n",
       "               Bedrooms  \n",
       "               -9191.94  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm(AdjSalePrice ~ poly(SqFtTotLiving, 2) + SqFtLot +\n",
    "   BldgGrade + Bathrooms +  Bedrooms, data=house_98105)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:12:23.282215Z",
     "start_time": "2019-04-15T16:12:22.957Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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TwajRYeHh4eHq6sagEAALRIMOg2AAAA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\nadgIEUIIURo2QoQQQpT2P2KP5WwilaTBAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Partial Residual plot\n",
    "df <- data.frame(SqFtTotLiving = house_98105[, 'SqFtTotLiving'],\n",
    "                 Terms = terms[, 1],\n",
    "                 PartialResid = partial_resid[, 1])\n",
    "ggplot(df, aes(SqFtTotLiving, PartialResid)) +\n",
    "  geom_point(shape=1) + scale_shape(solid = FALSE) +\n",
    "  geom_smooth(linetype=2) + \n",
    "  geom_line(aes(SqFtTotLiving, Terms))+\n",
    "  theme_bw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Splines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:14:21.422086Z",
     "start_time": "2019-04-15T16:14:21.381Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = AdjSalePrice ~ bs(SqFtTotLiving, knots = knots, \n",
       "    degree = 3) + SqFtLot + Bathrooms + Bedrooms + BldgGrade, \n",
       "    data = house_98105)\n",
       "\n",
       "Coefficients:\n",
       "                                  (Intercept)  \n",
       "                                   -414157.61  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)1  \n",
       "                                   -199529.76  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)2  \n",
       "                                   -120580.64  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)3  \n",
       "                                    -71644.39  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)4  \n",
       "                                    195677.89  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)5  \n",
       "                                    845244.25  \n",
       "bs(SqFtTotLiving, knots = knots, degree = 3)6  \n",
       "                                    695545.67  \n",
       "                                      SqFtLot  \n",
       "                                        33.33  \n",
       "                                    Bathrooms  \n",
       "                                     -4778.21  \n",
       "                                     Bedrooms  \n",
       "                                     -5778.70  \n",
       "                                    BldgGrade  \n",
       "                                    134462.37  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(splines)\n",
    "knots <- quantile(house_98105$SqFtTotLiving, p=c(.25, .5, .75))\n",
    "lm_spline <- lm(AdjSalePrice ~ bs(SqFtTotLiving, knots=knots, degree=3) +  SqFtLot +  \n",
    "                  Bathrooms + Bedrooms + BldgGrade,  data=house_98105)\n",
    "lm_spline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Generalized Additive Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:17:46.266264Z",
     "start_time": "2019-04-15T16:17:45.158Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: nlme\n",
      "\n",
      "Attaching package: ‘nlme’\n",
      "\n",
      "The following object is masked from ‘package:dplyr’:\n",
      "\n",
      "    collapse\n",
      "\n",
      "This is mgcv 1.8-28. For overview type 'help(\"mgcv-package\")'.\n"
     ]
    }
   ],
   "source": [
    "library(mgcv)\n",
    "lm_gam <- gam(AdjSalePrice ~ s(SqFtTotLiving) + SqFtLot + \n",
    "                Bathrooms +  Bedrooms + BldgGrade, \n",
    "              data=house_98105)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-15T16:17:59.529947Z",
     "start_time": "2019-04-15T16:17:59.501Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Family: gaussian \n",
       "Link function: identity \n",
       "\n",
       "Formula:\n",
       "AdjSalePrice ~ s(SqFtTotLiving) + SqFtLot + Bathrooms + Bedrooms + \n",
       "    BldgGrade\n",
       "\n",
       "Estimated degrees of freedom:\n",
       "4.49  total = 9.49 \n",
       "\n",
       "GCV score: 30148051324     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm_gam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "R 3.5",
   "language": "R",
   "name": "ir35"
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  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.3"
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  "toc": {
   "nav_menu": {},
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